通过可调速度轨迹提升生成质量，无需重训练即可改进采样效果。
Velocity Scheduled Flow Matching
- 用可变速度曲线替代固定速度，设计新型流匹配采样路径。
- 在CIFAR-10上，采样速度优化使FID降低最多19.8%。
- 适用于已有模型的高效优化，尤其适合低计算量场景。
流匹配通过神经网络回归噪声与数据间线性插值的条件速度进行训练，而网络评估次数（NFE）决定了采样成本。传统线性插值隐含了全程恒定速度的设定。本文提出速度调度流匹配（VSFM），将条件目标 $x_1 - x_0$ 替换为 $v(t)(x_1 - x_0)$，其中 $v:[0,1] \to \mathbb{R}_{\geq 0}$ 为任意非负速度函数且满足 $\int_0^1 v\,dt = 1$。研究了六种来自运动规划的多项式速度曲线。首次应用在推理阶段：预训练的线性流匹配模型可通过非均匀 $τ$-调度积分实现任意可接受速度曲线的采样，无需重训练且无额外计算；在CIFAR-10上可使FID降低最高19.8%。从零开始以减速曲线训练，在4次NFE下进一步降低FID达17.4%。性能提升源于欧拉积分器在诱导网格上的局部截断误差。
原文摘要 · Abstract (English)
Flow matching trains a neural network to regress the conditional velocity along a linear interpolant between noise and data, and the number of network evaluations~(NFE) sets the cost of sampling. The straight-line interpolant carries an implicit choice: the sample moves at constant speed throughout the trajectory. We relax this choice and introduce Velocity Scheduled Flow Matching~(VSFM), which replaces the conditional target $x_1 - x_0$ with $v(t)(x_1 - x_0)$ for any nonnegative profile $v:[0,1]\to\mathbb{R}_{\geq 0}$ satisfying $\int_0^1 v\,dt = 1$. We study six polynomial profiles drawn from motion planning. The first use of VSFM is at inference time: a pretrained linear flow-matching model can be sampled under any admissible profile by integrating its ODE on a non-uniform $τ$-schedule, with no retraining and no additional computation; on CIFAR-10 this lowers FID by up to $19.8\%$. Training from scratch under a braking profile gives a further reduction of $17.4\%$ at $4$~NFE. Both gains follow from the local truncation error of the Euler integrator on the induced grid.
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